The present invention relates to a second harmonic generator (SHG) and a method of fabrication thereof, or more in particular to a second harmonic generator of waveguide type for converting a semiconductor laser beam about 800 nm in wavelength into a blue light about 400 nm in wavelength, which is suitable as a light source for optical disk units, laser printers and other optical devices.
An improved recording density of an optical recording and reproduction apparatus and a higher resolution of a laser beam printer have been expected by shortening the wavelength of the laser beam. Nevertheless, it is not easy to reduce the semiconductor laser wavelength from 800 nm to 500 nm or less, for example, because the semiconductor of III-V group so far used with the laser is required to be changed to the semiconductor of II-VI group.
For this reason, attention has been given to a method for converting an infrared ray like a semiconductor laser beam (infrared ray) 800 nm in wavelength into a second harmonic wave 400 nm in wavelength by use of optical non-linearity.
If a second harmonic wave is to be efficiently generated by a second harmonic generator like this, it is necessary to maintain the law of energy conservation and the law of conservation of momentum between the fundamental wave and the second harmonic wave.
In view of the fact that the refractive index of an optical material generally changes with wavelength, however, there occurs the problem that the law of conservation of momentum fails to hold between different wavelengths satisfying the law of energy conservation, thereby necessitating phase matching between the fundamental wave and the second harmonic wave.
The phase matching is defined as a phenomenon in which innumerable second harmonic wave components generated in a second harmonic generator are combined with each other with the same phase during the process of propagation in an optical waveguide.
The phase matching combines the second harmonic components generated, which are outputted in such a direction as to be intensified with each other.
There are suggested several methods of phase matching.
JP-A-61-18934, for example, as shown in FIG. 1, discloses a method in which an optical waveguide 12 is formed on a LiNbO.sub.3 single crystal substrate 11 by the proton exchange (a method of partially replacing Li ions of LiNbO.sub.3), and a fundamental wave 13 polarized along the direction perpendicular to the substrate surface is applied from an end thereof thereby to collect a second harmonic wave 14 polarized toward the direction perpendicular to the surface of the substrate generated by the Cherenkov radiation. According to this method, the second harmonic wave is in a mode for radiation from the waveguide outward, and therefore the phase matching requirement is met.
In a method using the Cherenkov radiation described above, the second harmonic wave 14 becomes crescent in form, thereby leading to a large wave aberration, and it is almost impossible to reduce it to a minute light spot usable for optical disk devices or the like.
A method called the angle phase matching is reported in the Preliminary Transactions C-249 for the 1989 Autumn Conference of Japan Electronics Information Communication Society.
According to the angle phase matching, as shown in FIG. 2, an optical waveguide 22 is formed by liquid phase growth of lithium niobate (MgO: LiNbO.sub.3) doped with magnesium on a lithium tantalate (LiTaO.sub.3) substrate 21. A fundamental wave 23 polarized (TE polarization) is applied in the direction z perpendicular to the substrate surface from an end of the optical waveguide 22, and a second harmonic wave 24 polarized (TE polarization) in the direction x parallel to the substrate surface is emitted from the other end thereof.
In the process of propagation of the fundamental wave 23 through the optical waveguide 22, the nonlinearity of refractive index causes the conversion of the fundamental wave 23 to second harmonic wave components. At the same time, to the extent that the fundamental wave 23 is equal to the second harmonic wave components in propagation rate, the second harmonic wave components are always outputted while being subjected to phase matching, and therefore a maximum output of second harmonic wave is produced.
In view of the fact that the refractive index changes in proportion to the light frequency, however, the condition for phase matching described above cannot be satisfied. The condition for phase matching described above cannot be met, for example, if the fundamental wave 23 and the second harmonic wave 24 are both polarized in the direction z. As shown in FIG. 2, therefore, the second harmonic wave 24 is polarized in the direction x to use a crystal having a refractive index in the direction satisfying the condition for phase matching. In other words, the phase matching is attained by utilizing the anisotropy of crystal.
In spite of this, the use of a ferroelectric material having a large nonlinear optical coefficient like LiNbO3 in the conventional method shown in FIG. 2 often makes it impossible to obtain a blue light due to an insufficient phase matching caused by dependence of refractive index on wavelength in the range of 500 nm or less of the second harmonic wave 24.
Further, the fundamental wave 23 and the second harmonic wave 24 are polarized in the directions at right angles to each other, so that the temperature coefficients of refractive index in the respective directions of polarization are considerably different from each other. As a result, the propagation rate is changed with temperature and the condition for phase matching fails to be met, so that the acceptance bandwidth of temperature is narrowed to about 0.1.degree. C. At the same time, an unrealistic value of, say, 0.01 .mu.m or less would be required of the film thickness precision of the optical waveguide 22.
On the other hand, Electronics Letters, Vol. 25, pp. 731 to 732 suggests, as shown in FIG. 3, a method in which a pole-inverted layer 35 with the direction of spontaneous polarization inverted at equal pitches and an optical waveguide 32 by the proton exchange are formed on a LiNbO.sub.3 substrate 31 or the like ferroelectric substance having a spontaneous polarization. A fundamental wave 33 polarized in the direction z to the substrate surface is applied from an end of the optical waveguide 32, and a second harmonic wave 34 polarized in the direction z is recovered from the other end thereof.
In this case, the intensity of the second harmonic wave components generated in the optical waveguide 32 is differentiated by the inversion of spontaneous polarization, and the length of the inversion pitch thereof is regulated thereby to subject the intensified second harmonic wave components to phase matching for recovery.
A method for generating a pole-inverted layer 35 by forming and heat-treating an SiO.sub.2 or TiO.sub.2 pattern on a LiNbO3 single crystal substrate 41 is disclosed in The IEEE Photonics Technology Letters, Vol. 1, No. 10, 1989, pp. 316 to 318.
FIGS. 4A to 4D are diagrams showing another process of forming the pole-inverted layer 35. First, as shown in FIG. 4A, a predetermined pattern 41' of Ti layer is formed by photo-lithography on the LiNbO.sub.3 substrate 41, and the Ti layer is diffused by heat treatment as shown in FIG. 4B thereby to form a Ti diffused layer 42
Miyazawa et al. report in The Journal of Applied Physics, Vol. 50, No. 7, 1979, pp. 4599 to 4603 that the Curie temperature of the Ti diffused layer 42 is reduced by about 20.degree. to 50.degree. C. as compared with that of the LiNbO3 substrate 41 depending on the Ti concentration.
The spontaneous polarization Ps of a ferroelectric substance like LiNbO.sub.3 can be expressed by equation (1), and the temperature dependence of the spontaneous polarization Ps of the single crystal substrate 41 and the Ti diffused layer 42 is given as shown in FIG. 5. It is thus seen that the Ti diffused layer 42 is smaller than the substrate 41 both in Curie temperature Tc' and magnitude of spontaneous polarization. C is a constant. ##EQU1## As a result, the heating at a temperature T.sub.0 lower than the Curie temperature Tc' of the Ti diffused layer 42 induces a negative charge at the boundary between the Ti diffused layer 42 and the substrate 41 due to the difference in spontaneous polarization as shown in FIG. 4B. This electric charge generates an electric field E along the direction of arrow as shown in FIG. 4C.
When the magnitude of the electric field E exceeds a threshold level specific to a ferroelectric substance, the spontaneous polarization of the surface is inverted thereby to form a pole-inverted layer 43. This pole-inverted layer 43 is held even when the temperature is restored from T.sub.0 to, say, room temperature.
The pole-inverted layer 43 is formed in extension toward the direction of the electric field E in proportion to the magnitude thereof.
The magnitude of the component of the electric field E in the direction of axis c is expressed by equation (1') below. ##EQU2## where .DELTA.Ps is a spontaneous polarization difference between the LiNbO.sub.3 crystal and the Ti diffused layer shown in FIG. 5, .epsilon. the dielectric constant along the direction of axis c of LiNbO.sub.3, d the thickness of the Ti diffused layer 42, and numeral l the thickness of the substrate 41. Also, .theta. is the angle formed between the tangent of the boundary between the Ti diffused layer 42 and the substrate 41 and the axis c of the LiNbO.sub.3 crystal.
According to the conventional method shown in FIGS. 4A to 4D, the pole inversion and internal diffusion of Ti proceed at the same time Especially, the fact that the diffusion in the direction parallel to the substrate surface (lateral diffusion) during heat treatment causes the diffused layer 42 to extend in lateral direction, and therefore the value of cos .theta. around the periphery of the diffused layer 42 becomes considerably large, with the result that the pole-inverted layer 43 also extends in lateral direction Thus, as shown in FIG. 4D, pole-inverted layers are connected in the form of triangular wave.
The Preliminary Transactions 27-a-P-2 for the 1990 Autumn Lecture Meeting of the Japan Applied Physics Society reports that Nb is used instead of the SiO.sub.2 or TiO.sub.2 pattern mentioned above.
A device formed in the manner mentioned above, though the output light thereof is not difficult to reduce unlike the device shown in FIG. 1, has an insufficient conversion efficiency from the fundamental wave 33 to the second harmonic wave 34 due to the triangular cross section thereof.
The study by the present inventors, on the other hand, shows an acceptance bandwidth of temperature of about 3.degree. C. which is not known. This value is larger than that (about 0.2.degree. C.) of the device configured as shown in FIG. 2, but is not yet sufficient for practical purposes.
With regard to an improved conversion efficiency, G. Arvidssonn et al, theoretically clarified in The Proceedings of International Conference on Materials for Nonlinear and Electro-optics, pp. 1 to 6, that the conversion efficiency to a second harmonic wave is increased four times or more and the positional accuracy of a pole-inverted layer can be relaxed if the pole-inverted layer 43 in the triangular wave shape shown in FIG. 4D is changed to a rectangular grating 63 as shown in FIG. 6.
The pole-inverted portion actually obtained in the conventional methods, however, has a cross section of triangular form as shown in FIG. 3 or 4D, and a device having a pole-inverted layer in perfect rectangular shape as suggested by the theory is not known as yet.